file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/CategoryTheory/Monoidal/Limits.lean | CategoryTheory.Limits.limLax_obj' | [] | [
118,
6
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117,
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Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.has_colimits_of_hasCoequalizers_and_coproducts | [] | [
371,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.ex_semanticallyEquivalent_not_all_not | [
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}
] | [
544,
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Mathlib/Topology/Connected.lean | connectedComponentIn_univ | [] | [
694,
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Mathlib/Order/Filter/Extr.lean | IsExtrFilter.comp_tendsto | [] | [
411,
88
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.integral_deterministic' | [
{
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Mathlib/Topology/Separation.lean | disjoint_nhds_nhds_iff_not_specializes | [
{
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"tactic": "rw [← nhdsSet_singleton, disjoint_nhdsSet_nhds, specializes_iff_mem_closure]"
}
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1571,
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Mathlib/Topology/SubsetProperties.lean | isCompact_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.30840\nπ : ι → Type ?u.30845\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\na : α\nf : Filter α\nhf : NeBot f\nhfa : f ≤ 𝓟 {a}\n⊢ 𝓟 {a} ≤ 𝓝 a",
"tactic": "simpa only [principal_singleton] using p... | [
398,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.toFun_eq_coe | [] | [
128,
6
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Mathlib/Algebra/Homology/Homology.lean | cyclesMap_id | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\nC₁ C₂ C₃ : HomologicalComplex V c\nf : C₁ ⟶ C₂\ni : ι\n⊢ Subobject.factorThru (cycles C₁ i) (Subobject.arrow (cycles C₁ i) ≫ Hom.f (𝟙 C₁) i)\n ... | [
216,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.hasFDerivWithinAt | [] | [
190,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/FixedPoints.lean | OrderHom.map_sInf_subset_fixedPoints_le | [] | [
262,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_eq_top | [] | [
530,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
9
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_add | [
{
"state_after": "F : Type ?u.24201\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.24210\ninst✝³ : LinearOrderedField α\ninst✝² : ConditionallyCompleteLinearOrderedField β\ninst✝¹ : ConditionallyCompleteLinearOrderedField γ\ninst✝ : Archimedean α\na : α\nb : β\nq : ℚ\nx y : α\n⊢ sSup (cutMap β x + cutMap β y) = induc... | [
254,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.sum_integral_adjacent_intervals_Ico | [
{
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Mathlib/Data/Finset/Sups.lean | Finset.Nonempty.of_disjSups_left | [
{
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.sub_apply | [] | [
683,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_X | [] | [
1129,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
1
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src/lean/Init/Core.lean | heq_of_heq_of_eq | [] | [
634,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
633,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.fst | [] | [
763,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_lt_right | [] | [
107,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Data/Real/NNReal.lean | NNReal.div_le_of_le_mul | [
{
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}
] | [
817,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node4L_lemma₄ | [
{
"state_after": "no goals",
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"tactic": "linarith"
}
] | [
1154,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/PEquiv.lean | PEquiv.coe_mk_apply | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.zero_apply | [] | [
396,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.one_apply | [] | [
37,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.codRestrict | [] | [
144,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MulEquiv.subgroupMap_symm_apply | [] | [
3476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Cast/Basic.lean | ext_nat'' | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.tmp_closedBall_div_subset | [
{
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359,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.symm_neg | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
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Mathlib/Data/Multiset/Basic.lean | Multiset.inter_le_left | [] | [
1773,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1772,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.ne_zero_of_mem_factors | [
{
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456,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Mathlib/Topology/Inseparable.lean | SeparationQuotient.preimage_image_mk_open | [
{
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454,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.coeff_toPowerSeries_symm | [] | [
1159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
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Std/Data/Nat/Gcd.lean | Nat.gcd_eq_zero_iff | [
{
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"state_before": "i j : Nat\nh : i = 0 ∧ j = 0\n⊢ gcd i j = 0",
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}
] | [
178,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
176,
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Mathlib/MeasureTheory/PiSystem.lean | IsPiSystem.insert_empty | [
{
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"tactic": "intro s hs ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Data/Nat/Interval.lean | Nat.decreasing_induction_of_not_bddAbove | [] | [
350,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_finset_sum | [
{
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1241,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.exists_card_eq | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_bound' | [
{
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167,
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.isCycle_formPerm | [
{
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166,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signBijAux_surj | [
{
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359,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.sumInv_pqr | [
{
"state_after": "no goals",
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"tactic": "simp only [sumInv, add_zero, insert_eq_cons, add_assoc, map_cons, sum_cons,\n map_singleton, sum_singleton]"
}
] | [
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34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_star | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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] |
Mathlib/Algebra/QuadraticDiscriminant.lean | exists_quadratic_eq_zero | [
{
"state_after": "case intro\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NeZero 2\na b c x : K\nha : a ≠ 0\ns : K\nhs : discrim a b c = s * s\n⊢ ∃ x, a * x * x + b * x + c = 0",
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104,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Order/Filter/Basic.lean | Filter.forall_in_swap | [] | [
231,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.preComp_ι | [
{
"state_after": "C : Type u\ninst✝² : Category C\nX Y : C\nf : X ⟶ Y\nZ : C\ng : Y ⟶ Z\ninst✝¹ : HasImage g\ninst✝ : HasImage (f ≫ g)\n⊢ lift (MonoFactorisation.mk (image g) (ι g) (f ≫ factorThruImage g)) ≫ ι g = ι (f ≫ g)",
"state_before": "C : Type u\ninst✝² : Category C\nX Y : C\nf : X ⟶ Y\nZ : C\ng : Y... | [
553,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.algEquiv_symm_mk' | [] | [
1076,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
8
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.range_mem_leftTransversals | [
{
"state_after": "case mk.intro.mk.intro\nG : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nf : G ⧸ H → G\nhf : ∀ (q : G ⧸ H), ↑(f q) = q\nq₁ q₂ : G ⧸ H\nh :\n Set.restrict (Set.range f) Quotient.mk'' { val := f q₁, property := (_ : ∃ y, f y = f q₁) } =\n Set.restrict (Set.range f) Quotient.mk''... | [
300,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean | Complex.tendsto_abs_tan_of_cos_eq_zero | [
{
"state_after": "x : ℂ\nhx : cos x = 0\n⊢ Tendsto (fun x => ‖sin x‖ / ‖cos x‖) (𝓝[{x}ᶜ] x) atTop",
"state_before": "x : ℂ\nhx : cos x = 0\n⊢ Tendsto (fun x => ↑abs (tan x)) (𝓝[{x}ᶜ] x) atTop",
"tactic": "simp only [tan_eq_sin_div_cos, ← norm_eq_abs, norm_div]"
},
{
"state_after": "x : ℂ\nhx :... | [
49,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.choose_spec | [] | [
3056,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3055,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ico | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.97957\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhcd : c ≤ d\nh : c ≤ b\n⊢ Iio b ∪ Ico c d = Iio (max b d)\n\ncase inr\nα : Type u_1\nβ : Type ?u.97957\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhcd : d ≤ c\nh : d ≤ b\n⊢ Iio b ∪ Ico c d = Iio (ma... | [
1395,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
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Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_positiveOrientation_of_isEmpty | [] | [
100,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.map_map | [
{
"state_after": "G : Type u\ninst✝⁴ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝³ : Group H\nI : Type u_1\ninst✝² : Group I\nM : Subgroup H\nO : Subgroup I\ninst✝¹ : Subgroup.Normal M\ninst✝ : Subgroup.Normal O\nf : G →* H\ng : H →* I\nhf : N ≤ Subgroup.comap f M\nhg : M ≤ Subgroup.coma... | [
271,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_reaches_rev | [
{
"state_after": "case refl\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂ → Prop\nH : Respects f₁ f₂ tr\na₁ : σ₁\na₂ : σ₂\naa : tr a₁ a₂\nb₂ : σ₂\n⊢ ∃ c₁ c₂, Reaches f₂ a₂ c₂ ∧ tr c₁ c₂ ∧ Reaches f₁ a₁ c₁\n\ncase tail\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂... | [
923,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.epi_iff_exact_zero_right | [
{
"state_after": "V : Type u\ninst✝⁴ : Category V\ninst✝³ : HasImages V\nA✝ B✝ C D : V\nf✝ : A✝ ⟶ B✝\ng : B✝ ⟶ C\nh✝ : C ⟶ D\ninst✝² : HasZeroObject V\ninst✝¹ : Preadditive V\ninst✝ : HasEqualizers V\nA B : V\nf : A ⟶ B\nh : Exact f 0\ne₁ : Epi (imageToKernel f 0 (_ : f ≫ 0 = 0))\n⊢ Epi f",
"state_before": ... | [
346,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.a_mono | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nL : E →L[𝕜] F\nr ε δ : ℝ\nh : ε ≤ δ\nx : E\nr' ... | [
156,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Algebra/DirectSum/Algebra.lean | DirectSum.algebraMap_toAddMonoid_hom | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.compl_mem_coclosedCompact_of_isClosed | [] | [
614,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.sup_toAddSubmonoid | [
{
"state_after": "case h\nR : Type u_2\nR₂ : Type ?u.109627\nK : Type ?u.109630\nM : Type u_1\nM₂ : Type ?u.109636\nV : Type ?u.109639\nS : Type ?u.109642\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMono... | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_id_eq_join₁ | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_map_iff | [] | [
272,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/List/Sublists.lean | List.pairwise_sublists | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α → Prop\nl : List α\nH : Pairwise R l\nthis : Pairwise (Lex (swap fun b a => R a b)) (sublists' (reverse l))\n⊢ Pairwise (fun l₁ l₂ => Lex R (reverse l₁) (reverse l₂)) (sublists l)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α... | [
369,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.antidiagonal_succ' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ antidiagonal (n + 1) = (n + 1, 0) ::ₘ map (Prod.map id Nat.succ) (antidiagonal n)",
"tactic": "rw [antidiagonal, List.Nat.antidiagonal_succ', ← coe_add, add_comm, antidiagonal, coe_map,\n coe_add, List.singleton_append, cons_coe]"
}
] | [
70,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.nat_even_mul_periodic | [] | [
389,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_eq_one | [] | [
375,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_int_mul_pi_sub | [] | [
1347,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousAt.continuousWithinAt | [] | [
844,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.corepresentable_of_nat_iso | [] | [
286,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Std/Data/String/Lemmas.lean | String.foldrAux_of_valid | [
{
"state_after": "α : Type u_1\nf : Char → α → α\nl m r : List Char\na : α\n⊢ foldrAux f a { data := l ++ List.reverse (List.reverse m) ++ r }\n { byteIdx := utf8Len l + utf8Len (List.reverse (List.reverse m)) } { byteIdx := utf8Len l } =\n List.foldr f a (List.reverse (List.reverse m))",
"state_bef... | [
701,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
693,
1
] |
Mathlib/Data/Dfinsupp/Lex.lean | Pi.lex_eq_dfinsupp_lex | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiff_of_differentiable_iteratedDeriv | [] | [
275,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | Nat.coprime.isPrimePow_dvd_mul | [
{
"state_after": "case inl\nR : Type ?u.12477\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n b : ℕ\nhn : IsPrimePow n\nhab : coprime 0 b\n⊢ n ∣ 0 * b ↔ n ∣ 0 ∨ n ∣ b\n\ncase inr\nR : Type ?u.12477\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n a b : ℕ\nhab : coprime a b\nhn : IsPrimePow n\nha : a ≠ 0\n⊢ n ∣ a * b ↔... | [
144,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.support_congr | [
{
"state_after": "ι : Type ?u.1119536\nα : Type u_1\nβ : Type ?u.1119542\nf g : Perm α\nx y : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : IsCycle f\nhg : IsCycle g\nh : support f ⊆ support g\nh' : ∀ (x : α), x ∈ support f → ↑f x = ↑g x\nthis : support f = support g\n⊢ f = g",
"state_before": "ι : Typ... | [
604,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.startPos | [] | [
807,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
806,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.bisim_simple | [
{
"state_after": "case left\nα : Type u\nβ : Type v\nδ : Type w\ns₁✝ s₂✝ : Stream' α\nhh : head s₁✝ = head s₂✝\nht₁ : s₁✝ = tail s₁✝\nht₂ : s₂✝ = tail s₂✝\ns₁ s₂ : Stream' α\nx✝ : (fun s₁ s₂ => head s₁ = head s₂ ∧ s₁ = tail s₁ ∧ s₂ = tail s₂) s₁ s₂\nh₁ : head s₁ = head s₂\nh₂ : s₁ = tail s₁\nh₃ : s₂ = tail s₂\n... | [
333,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.liftRel_subrelation_lex | [] | [
508,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iUnion_null | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nR : Type ?u.3292\nR' : Type ?u.3295\nms : Set (OuterMeasure α)\nm✝ : OuterMeasure α\ninst✝ : Countable β\nm : OuterMeasure α\ns : β → Set α\nh : ∀ (i : β), ↑m (s i) = 0\n⊢ ↑m (⋃ (i : β), s i) = 0",
"tactic": "simpa [h] using m.iUn... | [
119,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_mod_of_dvd | [
{
"state_after": "α : Type ?u.268594\nβ : Type ?u.268597\nγ : Type ?u.268600\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\nh : c ∣ b\n⊢ a % b % c = (b * (a / b) + a % b) % c",
"state_before": "α : Type ?u.268594\nβ : Type ?u.268597\nγ : Type ?u.268600\nr : α → α → Prop\ns : β → β →... | [
1095,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_Icc_left | [] | [
179,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/LocallyFinite.lean | Ioo_toDual | [
{
"state_after": "α : Type u_1\nβ : Type ?u.113900\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢ Ioo (↑toDual a) (↑toDual b) = Ioo b a",
"state_before": "α : Type u_1\nβ : Type ?u.113900\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢... | [
852,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Submodule.norm_coe | [] | [
2730,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2728,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.dvd_iff_prime_pow_dvd_dvd | [
{
"state_after": "case inl\nd : ℕ\n⊢ d ∣ 0 ↔ ∀ (p k : ℕ), Prime p → p ^ k ∣ d → p ^ k ∣ 0\n\ncase inr\nn d : ℕ\nhn : n ≠ 0\n⊢ d ∣ n ↔ ∀ (p k : ℕ), Prime p → p ^ k ∣ d → p ^ k ∣ n",
"state_before": "n d : ℕ\n⊢ d ∣ n ↔ ∀ (p k : ℕ), Prime p → p ^ k ∣ d → p ^ k ∣ n",
"tactic": "rcases eq_or_ne n 0 with (rfl... | [
657,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.one_mem | [] | [
250,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
11
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_push | [] | [
1111,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_iff_uIcc_subset | [] | [
269,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.shadow_monotone | [] | [
87,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.coe_equivMapOfInjective_apply | [] | [
620,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | singleton_mul_closedBall_one | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ {x} * closedBall 1 δ = closedBall x δ",
"tactic": "simp"
}
] | [
181,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.continuousWithinAt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.101350\nι : Type ?u.101353\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ : Set α\ninst✝ : PseudoMetricSpace β\nf : α → β\na : α\ns : Set α\n⊢ ContinuousWithinAt f s a ↔ ∀ (ε : ℝ), ε > 0 → ∃ δ, δ > 0 ∧ ∀ {x : α}, ... | [
1060,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | NNReal.tendsto_inverse_atTop_nhds_0_nat | [
{
"state_after": "α : Type ?u.1359\nβ : Type ?u.1362\nι : Type ?u.1365\n⊢ Tendsto (fun a => ↑(↑a)⁻¹) atTop (𝓝 ↑0)",
"state_before": "α : Type ?u.1359\nβ : Type ?u.1362\nι : Type ?u.1365\n⊢ Tendsto (fun n => (↑n)⁻¹) atTop (𝓝 0)",
"tactic": "rw [← NNReal.tendsto_coe]"
},
{
"state_after": "no goa... | [
45,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.lintegral_coeFn | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1574917\nγ : Type ?u.1574920\nδ : Type ?u.1574923\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α →ₘ[μ] ℝ≥0∞\n⊢ (∫⁻ (a : α), ↑f a ∂μ) = lintegral ... | [
854,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Left.inv_lt_self | [] | [
465,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ cos ↑π = -1",
"tactic": "rw [cos_coe, Real.cos_pi]"
}
] | [
402,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.t1Space | [
{
"state_after": "case h.e'_3\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\nh : IsClosed {1}\nx : G\n⊢ {x} = (fun x_1 => x_1 * x) '' {1}",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\n... | [
1419,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/Topology/Filter.lean | Filter.mem_interior | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.15646\nα : Type u_1\nβ : Type ?u.15652\nX : Type ?u.15655\nY : Type ?u.15658\ns : Set (Filter α)\nl : Filter α\n⊢ l ∈ interior s ↔ ∃ t, t ∈ l ∧ Iic (𝓟 t) ⊆ s",
"tactic": "rw [mem_interior_iff_mem_nhds, mem_nhds_iff]"
}
] | [
163,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
11
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_mul' | [] | [
981,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Logic/Basic.lean | forall_apply_eq_imp_iff₂ | [] | [
820,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
9
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_mem | [] | [
983,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
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